(r-5)(r-3)=

Solution for (r-5)(r-3)= equation:

Simplifying
(r + -5)(r + -3) = 0

Reorder the terms:
(-5 + r)(r + -3) = 0

Reorder the terms:
(-5 + r)(-3 + r) = 0

Multiply (-5 + r) * (-3 + r)
(-5(-3 + r) + r(-3 + r)) = 0
((-3 * -5 + r * -5) + r(-3 + r)) = 0
((15 + -5r) + r(-3 + r)) = 0
(15 + -5r + (-3 * r + r * r)) = 0
(15 + -5r + (-3r + r2)) = 0

Combine like terms: -5r + -3r = -8r
(15 + -8r + r2) = 0

Solving
15 + -8r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + -1r)(5 + -1r) = 0

Subproblem 1
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {3, 5}